Hydrodynamic origins of symmetric swimming strategies

TL;DR

This paper reveals that symmetric and anti-symmetric swimming strokes are hydrodynamically equivalent and optimal in viscous fluids, explaining the natural prevalence of symmetric gaits through a physical efficiency principle.

Contribution

It introduces a hydrodynamic duality showing symmetric and anti-symmetric strokes are equally efficient and optimal, supported by numerical simulations in viscous environments.

Findings

Symmetric and anti-symmetric strokes are dynamically equivalent.

Both stroke types are proven to be optimal for efficiency.

Results hold in three-dimensional body plans.

Abstract

Efficient locomotion is important for the evolution of complex life, yet the physical principles selecting specific swimming strokes often remain entangled with biological constraints. In viscous fluids, the scallop theorem constrains the temporal organization of strokes, but no analogous principle is known for their spatial structure, leaving the prevalence of symmetric gaits across diverse organisms without a physical explanation. Here we show that spatial symmetry acts as an emergent organizing principle for efficiency in viscous fluids. By analysing deformable swimmers whose strokes are not constrained to any particular symmetry class, we identify a hydrodynamic duality: symmetric and anti-symmetric strokes are dynamically equivalent, yielding identical speeds and efficiencies, which we prove are optimal among all strokes. We validate this using numerical simulations of Stokes flow, demonstrating that these symmetry rules persist even in three-dimensional body plans. Our results suggest that the prevalence of symmetric and alternating gaits in nature reflects not merely a developmental constraint, but a physical optimality principle for locomotion in viscous environments, complementing developmental and neural constraints.